If the clematis are hybrids rather than species, move in September/October. If they've been in longer than 3 or 4 years, they'll have a large root system, so you need to try to dig it out more or less intact by starting at least a foot out from the base of the plant all round, with a garden fork, gently levering the soil, till you discover the extent of the rootballs. Make sure the new planting holes are large enough to accommodate the roots without cramping or bending them to make them fit and water in well. Doesn't matter if you bury them slightly deeper than they were originally, but don't leave them higher than they were.
If you have species such as montana, and they've been in more than 5 years and the plant has a very woody 'trunk', use the same method, but you may find they don't transplant well.

Clems can be difficult to move, and die on you. They don't like root disturbance, so as Bamboo says, get ALL the rootball out if you possibly can.